Finite Group Databasebeta

← #20244455

Subgroups — #20244455

Order 6016.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689923C211yesmaximal, characteristic, complemented
2#15689634C212yesmaximal, complemented
3#15689139C212yesmaximal, complemented
4#15688880C211yesmaximal, characteristic, complemented
5C47×#407C211yesmaximal, characteristic, complemented
6C2×#10625350C2212yes—
7#13094057—22no—
8#13094052—22no—
9#13094046—22no—
10#13094007—22no—
11#13094003—22no—
12#13093998—22no—
13#13093993—22no—
14C4×C22⋊D47—24no—
15#13093983C2212yes—
16#13093950—24no—
17C23×C4×C47C2211yescharacteristic
18C2×M16×C47C2211yescharacteristic
19C2×M16×C47C2211yescharacteristic
20C22⋊C8×C47—22no—
21C24×C47D411yescharacteristic
22C22×C4×C47—22no—
23C22×C4×C47—22no—
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—24no—
29C2×C22⋊D47—22no—
30#10625350—22no—
31#10625350—22no—
32#10625350—22no—
33#10625350—22no—
34C2×D188D412yescomplemented
35C2×C4×D47—22no—
36C2×Dic94D412yescomplemented
37M16×C47—22no—
38M16×C47—22no—
39C2×C8×C47—21no—
40C2×C8×C47D412yescomplemented
41C22⋊Dic47—24no—
42C22⋊Dic47—22no—
43(C2×D47)⋊C4—24no—
44C4⋊Dic47—22no—
45Dic47⋊C4—24no—
46C4×Dic47D414yescomplemented
47Dic188—22no—
48D376—22no—
49#10625325—24no—
50C23×C47—22no—
51C23×C47—21no—
52C23×C47—42no—
53C23×C47C2×D411yescharacteristic
54C22×D47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—42no—
59C2×C4×C47—41no—
60C2×C4×C47C2×D412yes—
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C22⋊D47—48no—
65C22⋊D47—42no—
66C22⋊D47—42no—
67C2×Dic47—24no—
68C2×Dic47—22no—
69D188—22no—
70D188—22no—
71C4×D47—42no—
72C4×D47—42no—
73Dic94—22no—
74Dic94—22no—
75C8×C47—22no—
76C8×C47—41no—
77C22×C47—24no—
78C22×C47—22no—
79C22×C47—41no—
80C22×C47—42no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47#12012yes—
84C22×C47#12111yescharacteristic
85C2×D47—44no—
86C2×D47—42no—
87C4×C47—41no—
88C4×C47#12011yescharacteristic
89C4×C47#12112yes—
90C4×C47#12711yescharacteristic
91Dic47—44no—
92Dic47—42no—
93#2010—471nomaximal, Sylow
94C2×C47—22no—
95C2×C47—21no—
96C2×C47—42no—
97C2×C47#39211yescharacteristic
98D47—82no—
99#575—471no—
100#525—472no—
101#421—472no—
102#407D4711yescharacteristic, complemented
103H(3,ℤ/4)—471no—
104C47#201011yescharacteristic, complemented, Sylow
105C2×#41—472no—
106C23×C4C2×D4711yescharacteristic
107#137—942no—
108AGL(1,ℤ/8)—942no—
109#135—942no—
110C2×M16C2×D4711yescharacteristic
111C2×M16C2×D4711yescharacteristic
112#123—942no—
113C22⋊Q8—942no—
114#121—942no—
115#120—942no—
116C4×D4—944no—
117#117—472no—
118#104—944no—
119C22⋊C8—22no—
120C24D18811yescharacteristic
121#41—942no—
122#41—942no—
123#41—942no—
124#41—942no—
125C2×Q8—472no—
126C2×D4—472no—
127C2×D4—944no—
128C2×D4—942no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—942no—
134C22×C4D18811yescharacteristic
135C22×C4C22×D4711yescharacteristic
136Q16—942no—
137SD16—944no—
138D8—942no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D4712yescomplemented
143C4⋊C4—944no—
144C4⋊C4—942no—
145C22⋊C4—944no—
146C22⋊C4—944no—
147C22⋊C4—942no—
148C42—474no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—942no—
153C23C2×D18811yescharacteristic
154Q8—942no—
155Q8—942no—
156D4—942no—
157D4—942no—
158D4—1888no—
159D4—1882no—
160D4—1882no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—944no—
167C2×C4—942no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4#1062535011yescharacteristic
171C2×C4D4×D4712yes—
172C2×C4D4×D4712yes—
173C2×C4C2×C22⋊D4711yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—1884no—
183C22—1882no—
184C22#1309399412yes—
185C22#1309399811yescharacteristic
186C4—41no—
187C4—1884no—
188C4—1882no—
189C4#1309399211yescharacteristic
190C4#1309399712yes—
191C4#1309402011yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—3762no—
196C2#1568903211yescharacteristic
subgroupG/H
centerC4#13094020
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC2×C47#392
hypercenter#407D47
hypocenterC47#2010
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689923C2semidirect
2. #15689634C2semidirect
3. #15689139C2semidirect
4. #15688880C2semidirect
5. C47×#407C2semidirect
34. C2×D188D4semidirect
36. C2×Dic94D4semidirect
40. C2×C8×C47D4semidirect
46. C4×Dic47D4semidirect
102. #407D47semidirect
104. C47#2010semidirect
142. C2×C8C22⋊D47semidirect